An oxide of an element is a gas and dissolves in water to give an acidic solution. The element belongs to

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

The uncertainty in the location of a circulating electron is equal to its de-Broglie wavelength. The minimum percentage error in the measurement of its velocity under these circumstances will be approximately:

The coordinates of the point $P$ on the curve $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$,where the tangent is inclined at an angle $\frac{\pi}{4}$ to the $x$-axis,are

$\sinh^{-1}(2^{3/2})$ is equal to :

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to